Chapter 14.3, Problem 22E

(a)

To determine

To calculate: The marginal productivity of x if the Cobb-Douglas production function for a company is given by $z=300x^{2/3}{y}^{1/3}$ where x is the company’s capital investment and y is the size of the labor force (in work-hours).

(b)

To determine

To calculate: The marginal productivity of x if the current labor force is $729$ work-hours and also plot the result.

(c)

To determine

To calculate: The marginal productivity of y if the Cobb-Douglas production function for a company is given by $z=300x^{2/3}{y}^{1/3}$ where x is the company’s capital investment and y is the size of the labor force (in work-hours).

(d)

To determine

To calculate: The marginal productivity of y if the current capital investment is $\$27,000$ and also plot the result.

(e)

To determine

The interpretation of graphs in parts (b) and (d) with regard to what they say about the effects on productivity of increased capital investment and of an increased labor force.